Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity

TL;DR

This paper develops a new path integral approach using coherent states to derive effective dynamics from full Loop Quantum Gravity, reproducing Loop Quantum Cosmology results and resolving the big-bang singularity.

Contribution

It introduces a novel discrete path integral formula for full LQG and connects it to LQC effective dynamics through semiclassical approximation.

Findings

Reproduces LQC effective dynamics in the $$-scheme.

Demonstrates resolution of big-bang singularity with a big bounce.

Provides a new framework linking full LQG to cosmological models.

Abstract

A new routine is proposed to relate Loop Quant Cosmology (LQC) to Loop Quantum Gravity (LQG) from the perspective of effective dynamics. We derive the big-bang singularity resolution and big bounce from the first principle of full canonical LQG. Our results are obtained in the framework of the reduced phase space quantization of LQG. As a key step in our work, we derive with coherent states a new discrete path integral formula of the transition amplitude generated by the physical Hamiltonian. The semiclassical approximation of the path integral formula gives an interesting set of effective equations of motion (EOMs) for full LQG. When solving the EOMs with homogeneous and isotropic ansatz, we reproduce the LQC effective dynamics in $\mu_0$-scheme. The solution replaces the big-bang singularity by a big bounce. In the end, we comment on the possible relation between the $\bar{\mu}$-scheme of effective dynamics and the continuum limit of the path integral formula.